Surfaces over Dirichlet Tessellations
Computer Aided Geometric Design
Image warping by radial basis functions: applications to facial expressions
CVGIP: Graphical Models and Image Processing
Multiresolution analysis of arbitrary meshes
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Image metamorphosis using snakes and free-form deformations
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Contour interpolation and surface reconstruction of smooth terrain models
Proceedings of the conference on Visualization '98
A transfinite form of Sibson's interpolant
Discrete Applied Mathematics - Special issue on the 13th European workshop on computational geometry CG '97
Voronoi-based interpolation with higher continuity
Proceedings of the sixteenth annual symposium on Computational geometry
Developments in bivariate spline interpolation
Journal of Computational and Applied Mathematics - Special issue on numerical analysis in the 20th century vol. 1: approximation theory
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
A framework for geometric warps and deformations
ACM Transactions on Graphics (TOG)
Digital Image Warping
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods
SIAM Journal on Scientific Computing
Scattered Data Interpolation with Multilevel B-Splines
IEEE Transactions on Visualization and Computer Graphics
Image Warping with Scattered Data Interpolation
IEEE Computer Graphics and Applications
Generalized barycentric coordinates on irregular polygons
Journal of Graphics Tools
Computer Aided Geometric Design
A quadrilateral rendering primitive
Proceedings of the ACM SIGGRAPH/EUROGRAPHICS conference on Graphics hardware
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
A geometric construction of coordinates for convex polyhedra using polar duals
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
A general geometric construction of coordinates in a convex simplicial polytope
Computer Aided Geometric Design
GI '07 Proceedings of Graphics Interface 2007
Spherical barycentric coordinates
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
On transfinite barycentric coordinates
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
GPU-assisted positive mean value coordinates for mesh deformations
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
ACM SIGGRAPH 2008 papers
Transfinite mean value interpolation
Computer Aided Geometric Design
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Coordinates for instant image cloning
ACM SIGGRAPH 2009 papers
Transfinite mean value interpolation in general dimension
Journal of Computational and Applied Mathematics
Interactive image deformation using cage coordinates on GPU
Proceedings of the 8th International Conference on Virtual Reality Continuum and its Applications in Industry
Pointwise radial minimization: Hermite interpolation on arbitrary domains
SGP '08 Proceedings of the Symposium on Geometry Processing
Maximum entropy coordinates for arbitrary polytopes
SGP '08 Proceedings of the Symposium on Geometry Processing
Interior distance using barycentric coordinates
SGP '09 Proceedings of the Symposium on Geometry Processing
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Controllable conformal maps for shape deformation and interpolation
ACM SIGGRAPH 2010 papers
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Barycentric interpolation and mappings on smooth convex domains
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Computer Aided Geometric Design
Model transduction for triangle meshes
Journal of Computer Science and Technology
Technical Section: Skeleton driven animation based on implicit skinning
Computers and Graphics
Better bases for radial basis function interpolation problems
Journal of Computational and Applied Mathematics
Transfinite surface interpolation over irregular n-sided domains
Computer-Aided Design
Positive Gordon-Wixom coordinates
Computer-Aided Design
Multicage image deformation on GPU
Proceedings of the 10th International Conference on Virtual Reality Continuum and Its Applications in Industry
Natural image composition with inhomogeneous boundaries
PSIVT'11 Proceedings of the 5th Pacific Rim conference on Advances in Image and Video Technology - Volume Part II
The Bernstein polynomial basis: A centennial retrospective
Computer Aided Geometric Design
Embedding a triangular graph within a given boundary
Computer Aided Geometric Design
Topologically correct reconstruction of tortuous contour forests
Computer-Aided Design
Computer Graphics Forum
Technical note: Signed Lp-distance fields
Computer-Aided Design
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Implicit skinning: real-time skin deformation with contact modeling
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
eHeritage of shadow puppetry: creation and manipulation
Proceedings of the 21st ACM international conference on Multimedia
eHeritage of shadow puppetry: creation and manipulation
Proceedings of the 21st ACM international conference on Multimedia
Video retargeting combining warping and summarizing optimization
The Visual Computer: International Journal of Computer Graphics
PolyCut: monotone graph-cuts for PolyCube base-complex construction
ACM Transactions on Graphics (TOG)
Footwear bio-modelling: An industrial approach
Computer-Aided Design
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
A comparison of Filippov sliding vector fields in codimension 2
Journal of Computational and Applied Mathematics
Bijective composite mean value mappings
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
Interactive ray casting of geodesic grids
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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Barycentric coordinates for triangles are commonly used in computer graphics, geometric modeling, and other computational sciences because they provide a convenient way to linearly interpolate the data that is given at the corners of a triangle. The concept of barycentric coordinates can also be extended in several ways to convex polygons with more than three vertices, but most of these constructions break down when used in the nonconvex setting. Mean value coordinates offer a choice that is not limited to convex configurations, and we show that they are in fact well-defined for arbitrary planar polygons without self-intersections. Besides their many other important properties, these coordinate functions are smooth and allow an efficient and robust implementation. They are particularly useful for interpolating data that is given at the vertices of the polygons and we present several examples of their application to common problems in computer graphics and geometric modeling.